[Lovera]

"A delayed overcall is one made by a player who has already passed. The bid is ordinarily inserted when there are signs that the opponent's bid is nearing its end. Thus:(20)♠KQ10863 ♥9 ♦764 ♣Q32 1♥ p 1NT p, 2♥ Bid 2♠ - Opponents' apparent intention not to go beyond a partial contract, it suggests that the partner has a good score and that he did not interfere due to his insufficient distributional strength. Since the overcall is delayed with the above assumptions, the overcall's partner must refrain from taking further offensive initiatives, because the overcall has already taken into due account the strength, albeit unrevealed, possessed by his partner. Thus:(21) ♠A75 ♥K853 ♦A92 ♣J85 1♥ p 1NT p, 2♥ 2 ♠ p p Remember that your partner was unable to overcall the first time. He states now to save us a difficult decision.(22) ♠AF876 ♥9 ♦K1064 ♣Q32 1♥ p 1NT p, 2♥ p p Bid 2♠ - The delayed overcall must be particularly used in duplicate, so as not to allow the opponents to take away precious partial scores" (From The Complete Stayman Systeme Of Contract Bidding pagg.239,240).On this topic I haven't found much out there that further specifies or extends its use to other levels and therefore I also add what Ron Klinger indicated on his site Partscore Competitive Bidding by Ron Klinger: https://csbnews.org/...by-ron-klinger/
(Lovera)

[Lovera]

Since the purpose of the topic is to better define the use of this type of bid also at other levels, I invite those who have used it to provide the data of their hand, of the bid and of the reason why they initially decided to pass for then, in the second round, bring the bid to level three/four.(Lovera)

[gszes]

The given auction does not seem to apply to the concept you are discussing. There appears to be little to no reason why the delayed 2s bidder did not bid 1s 2s (my choice) or even 3s (Every Hand An Adventure) immediately after the 1h opening bid. Maybe I misread it sigh.

[Cyberyeti]

The only delayed overcall we regularly use is after 1♣(2+) where we pass then bid 2♣ natural, also certain 2 suited bids show "clubs and ..." 2nd time round

[pescetom]

gszes, on 2024-February-12, 14:50, said:

Maybe I misread it sigh.

The post is already cryptic without the confusing textual auctions... Lovera please revise OP with hand diagrams if you want a meaningful dialogue.

Cyberyeti, on 2024-February-12, 15:40, said:

The only delayed overcall we regularly use is after 1♣(2+) where we pass then bid 2♣ natural

This, but also the same after 1♦(4+)... in both cases assuming partner has not overcalled in which case the cue is a raise.

[Lovera]

gszes, on 2024-February-12, 14:50, said:

The given auction does not seem to apply to the concept you are discussing. There appears to be little to no reason why the delayed 2s bidder did not bid 1s 2s (my choice) or even 3s (Every Hand An Adventure) immediately after the 1h opening bid. Maybe I misread it sigh.

The Stayman system use to bid immediatly 2♠ as weak jump overcall (6-4). Anyhow the hand is very weak and is bidded in delayed way. About the 3♠ is used for 7.th hand suit.